Dynamic analysis  of a free  vibrating  cantilever  beam

Abstract

This paper has as subject a theoretical, numerical and experimental study of the behavior of a 1.5 meters long and cross section of 0.02 meters wide and high beam. The main objective was to analyze a structure, in this case it was a cantilever steel beam, to establish the possible solutions that best define the behavior of this structure, to obtain the results and to prove the veracity of the results obtained by means of an experimental analysis method. In this sense, essential theoretical foundations were used for the understanding and realization of the mathematical formulations of this project, in order to obtain the analytical results of the vibration modes of the beam and respective natural frequencies. To complement the analysis of the beam behavior, the finite element method procedure was applied using the ansys software to obtain more accurate results. The results obtained for the beam from these two methodologies include bending modes among the first 10 degrees of freedom. To validate the study done previously a physical model of the beam was used for the experimental test, for this it was defined that the equipment for measuring the resonance frequencies would be a digital stroboscope, enabling the measurement of only 8 vibration modes due to its small frequency range.